Creating a matrix that calculates inverse and determinants without using the det and inv commands

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Rafaela Stylianou
Rafaela Stylianou 2016-10-24
编辑： Walter Roberson 2018-10-22
Hi, i have the following question:
Create a function that calculates the determinant and the inverse of a generic 2 X 2 matrix
The function should be named invanddet2by2. The function takes a generic 2 X 2 matrix as input, and returns two outputs: the determinant and the inverse. It should do the following few things:
It calculates the determinant
If the determinant is zero, the inverse is set to be an empty matrix (i.e. you assign the value [], that's squared brackets with no values inside, which for Matlab means an empty matrix)
If the determinant is non-zero, then it calculates the inverse
So far i have
M=[ 4 5;6 9]
d_correct=(M(1,1)*M(2,2))-(M(1,2)*M(2,1))
if d_correct==0
B=[0 0; 0 0]
else
Diagonal=[9 -5;-6 4]
Minv_correct=d_correct *(1./M)
'end'
and my codes fail the test for the inverse of the singular matrix and for the determinant of the singular matrix
Does anyone have an idea of what's gooing wrong?
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James Tursa
James Tursa 2016-10-25
编辑：James Tursa 2016-10-25
Create a file in your working directory called invanddet2by2.m, e.g.
edit invanddet2by2.m
In that file, put the following function code (some function wrapper code with your code inside):
% Insert comments here describing function purpose, inputs, and outputs
function [B,d_correct] = invanddet2by2(M)
d_correct = (M(1,1)*M(2,2))-(M(1,2)*M(2,1));
if d_correct==0
B = [0 0; 0 0]; <-- Fix this line to return the empty matrix [] instead of a 0's matrix
else
Diagonal = [9 -5;-6 4]; <-- Fix this line to be a generic formula of M elements, not hard-coded values
Minv_correct = d_correct *(1./M); <-- Fix this line to use Diagonal, do the division in the correct order, and assign to B
end
Make changes and corrections to the lines that I have indicated.
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Tai Lopez
Tai Lopez 2018-10-21
编辑：Walter Roberson 2018-10-22
I'm having a similar problem. so I've created a function, it works when I type any 2x2 matrix but it doesn't run. do you know what is wrong with it? I've also attached a picture which shows the error. This is what I have:
function [Inverse, Determinant] = invanddet2by2(M)
% INVANDDET2BY2 Calculates the determinant and the inverse of a 2 X 2 matrix.
% It calculates the determinant.
% If the determinant is zero, the inverse is set to be an empty matrix.
% If the determinant is non-zero, then it calculates the inverse
Determinant = (M(1,1)*M(2,2))-(M(1,2)*M(2,1))
if Determinant==0
Inverse = [];
else
Madj_correct = trace(M)*eye(size(M)) -
Steven Lord
Steven Lord 2018-10-21
You call your function with 0 input arguments. MATLAB doesn't know what it should use as the M matrix in your function. Call it and pass your matrix in as the input.

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更多回答（2 个）

Chaya N
Chaya N 2016-10-25
编辑：Chaya N 2016-10-25
A singular matrix, by definition, is one whose determinant is zero. hence, it is non-invertible. In code, this would be represented by an empty matrix. Therefore (using the same variable name as in your code),
B = [];
For a non-singular matrix M, recall that M * inverse(M) = I, the identity matrix. This is the simplest expression you could use to generate your inverse matrix. Therefore,
Minv_correct = eye(size(M))/M; % Note that this is regular division, NOT element-wise operation
There is also another commonly used method, that involves the adjoint of a matrix and the determinant to compute the inverse as inverse(M) = adjoint(M)/determinant(M). This involves the additional step of computing the adjoint matrix. For a 2 x 2 matrix, this would be computed as adjoint(M) = trace(M)*I - M. Therefore,
Madj_correct = trace(M)*eye(size(M)) - M;
Minv_correct = Madj_correct/d_correct;
You could use either of the above methods to compute your inverse matrix.
Walter Roberson
Walter Roberson 2016-10-25
In the case of the determinant being 0, you are not setting the inverse to the empty matrix.
You are not using the variable Diagonal .
Your formula for obtaining the inverse from the determinant is incorrect. See https://en.wikipedia.org/wiki/Invertible_matrix#Analytic_solution

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